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<p style="margin: 0px 0px 0px 23px;">The Axes of Rotation are the three axes around which the rotations of yaw, pitch and roll are applied w.r.t. the top-disk fixed reference system. The usage of this axes is very important in order to obtain a good cueing performance.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">Each axis is univocally defined by the distance from the top disk center using the following parameters:</p>
<p style="margin: 0px 0px 0px 23px;">Yaw rotation axis: X and Y distance.</p>
<p style="margin: 0px 0px 0px 23px;">Pitch rotation axis: X and Z distance.</p>
<p style="margin: 0px 0px 0px 23px;">Roll rotation axis: Y and Z distance.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The final values for these parameters are a consequence of cockpit installation on the platform as well as vehicle/suspension properties. Since different vehicle models can be driven on the same cockpit, and different cockpits can be installed on the top disk of the platform, the AoR computation must take into account a chain of offsets.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">Accordingly to the template spreadsheet included in VI-DriveSim installation (<span style="font-style: italic;">Cueing_computation_Template.xlsx</span>, at the sheet <span style="font-style: italic;">AoR Computation</span>), the following data must be known, measured or eventually estimated:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Driver hip on motion platform w.r.t. top disk origin</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="font-style: italic;">X_Hip_Dim &nbsp; – &nbsp; Y_Hip_Dim &nbsp; – &nbsp; Z_Hip_Dim &nbsp; [mm]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">This set of coordinates defines the distance from the hips of the driver on the cockpit to the center of the motion platform top disk, whose origin is on top disk center with right hand convention (X positive towards the front, Y positive to the left, Z positive upwards). The distance is measured (physically or by means of a CAD model) from the center of the seat.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: center; margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_01" width="453" height="363" style="margin:0px auto 0px auto;width:453px;height:363px;border:none" src="drvsim_aor_01.png"/></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Driver hip on the CAR w.r.t. front axle (X positive towards the front), vehicle centerline (Y positive to the left), at ground level (Z positive upwards)</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="font-style: italic;">X_Hip_Car &nbsp; – &nbsp; Y_Hip_Car &nbsp; – &nbsp; Z_Hip_Car &nbsp; &nbsp; &nbsp;[mm]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">These coordinates define the hip point of the driver on the real car and they must be expressed in right hand convention w.r.t. the origin on the front axle (X positive towards the front), vehicle centerline (Y positive to the left), at ground level (Z positive upwards). This measure must be consistent with the previous one (driver hip on motion platform), i.e. the same driver seat position should be used.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: center; margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_02" width="424" height="173" style="margin:0px auto 0px auto;width:424px;height:173px;border:none" src="drvsim_aor_02.png"/></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Car CG w.r.t. front axle (X positive towards the front), vehicle centerline (Y positive to the left), at ground level (Z positive upwards)</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="font-style: italic;">X_CG &nbsp; – &nbsp; Y_CG &nbsp; – &nbsp; Z_CG &nbsp; [mm]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">Once the measures are available the AoR can be computed accordingly to the following guideline:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Car CG and platform yaw axis</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">A reasonable approximation of the yaw axis of the car can be considered the center of gravity. Knowing the position of the CG in right hand convention w.r.t. the origin on the front axle (X positive towards the front), vehicle centerline (Y positive to the left), at ground level (Z positive upwards), it is possible to calculate the position of the yaw axis for the platform, to be inserted in VI-DriveSim interface:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_01" width="401" height="46" style="float:left;margin:0;width:401px;height:46px;border:none" src="drvsim_aor_eq_01.png"/> &nbsp; &nbsp; &nbsp; &nbsp; Unit: <span style="font-style: italic;">[m]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Car roll centers and platform roll axis</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The roll center height (from ground plane) of each axle must be known to calculate the distance from the CG of the sprung mass of the car to the roll axis, which in turn is used to compute the vertical offset of the roll axis for platform movement.</p>
<p style="margin: 0px 0px 0px 23px;">For the roll centers, nominal/static values are typically used, relative to the static ride height and considered on the same lateral coordinate of the CG.</p>
<p style="margin: 0px 0px 0px 23px;">With VI-SuspensionGen utility, it is possible to recover the roll center height for each suspension model w.r.t suspension travel and to get its value at static ride height.</p>
<p style="margin: 0px 0px 0px 23px;">Alternatively, these quantities can be estimated from the combination of the splines describing the Y-coordinate variation of a suspension w.r.t. the relative wheel travel (Wheel Location tab of suspension subsystems in VI-CarRealTime) and the splines describing the variation of camber with jounce.</p>
<p style="margin: 0px 0px 0px 23px;">Considering these splines, the variation of track with jounce at the contact patch can be calculated as:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: left; line-height: 1.28; margin: 0px 0px 11px 23px;"><img alt="drvsim_motioncueing_FormulaDeltaTrack" width="449" height="21" style="margin:0;width:449px;height:21px;border:none" src="drvsim_motioncueing_formuladeltatrack.png"/></p>
<p style="margin: 0px 0px 0px 23px;">With a simplified formulation, the roll center height is computed with:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_02" width="123" height="48" style="margin:0;width:123px;height:48px;border:none" src="drvsim_aor_eq_02.png"/> &nbsp; &nbsp; &nbsp; &nbsp;Unit: <span style="font-style: italic;">[mm]</span>  &nbsp; &nbsp; &nbsp; &nbsp; </p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;">&nbsp;</p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;">Where <span style="font-style: italic;">t</span> is the track width of the axle and dy/dz is the first derivative of the variation of track with jounce, calculated at the contact patch.<br />
Accordingly to the following picture, the distance from the CG of the sprung mass to the roll axis of the car can be calculated with:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_03" width="405" height="42" style="margin:0;width:405px;height:42px;border:none" src="drvsim_aor_eq_03.png"/> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Unit: <span style="font-style: italic;">[mm]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">Where <span style="font-style: italic;">h_RC_F</span> and<span style="font-style: italic;"> h_RC_R</span> are the roll center heights of front and rear suspension, respectively</p>
<p style="text-indent: -2px; margin: 0px 0px 0px 65px;"><span style="font-style: italic;"> h_CG_S</span> is the Z coordinate of the sprung mass CG from ground</p>
<p style="text-indent: 2px; margin: 0px 0px 0px 66px;"><span style="font-style: italic;">a_S</span> is the longitudinal distance of the sprung mass CG from the front axle</p>
<p style="text-indent: 1px; margin: 0px 0px 0px 65px;"><span style="font-style: italic;">WB</span> is the wheelbase of the car</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: center; margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_03" width="591" height="286" style="margin:0px auto 0px auto;width:591px;height:286px;border:none" src="drvsim_aor_03.png"/></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The roll axis for the platform, to be inserted in VI-DriveSim interface, is finally computed with:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_04" width="445" height="47" style="margin:0;width:445px;height:47px;border:none" src="drvsim_aor_eq_04.png"/> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Unit: <span style="font-style: italic;">[m]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 23px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span><span style="font-weight: bold;">Car pitch centers and platform pitch axis</span></p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The pitch center of the car is strictly linked to the anti-features of its suspension systems, as well as the drivetrain layout (driven wheels).</p>
<p style="margin: 0px 0px 0px 23px;">However, a generic procedure can be used to estimate and validate a nominal position for the pitch center, starting from a simple model of longitudinal suspension behavior, as described in the following pictures for a braking maneuver.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: center; margin: 0px 0px 0px 23px;"><img alt="drvsim_AoR" width="1093" height="320" style="margin:0px auto 0px auto;width:1093px;height:320px;border:none" src="drvsim_aor.png"/></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The pitch center is defined by the inclination of the antidive/antilift lines, where the longitudinal forces at contact patch create a vertical component reacted on the chassis.</p>
<p style="margin: 0px 0px 0px 23px;">The basic concept is that the wheelbase variation w.r.t. the relative suspension travel is proportional to the antidive/antilift percentages of the suspension itself, perpendicular to the direction where forces are applied.</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_05" width="53" height="45" style="margin:0;width:53px;height:45px;border:none" src="drvsim_aor_eq_05.png"/></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">In this way, the pitch center coordinates can be estimated from the combination of the splines describing the X-coordinate variation of a suspension w.r.t. the relative wheel travel (Wheel Location tab of suspension subsystems in VI-CarRealTime) and the splines describing the Side View Angle variation with jounce. </p>
<p style="margin: 0px 0px 0px 23px;">From these splines, it is possible to estimate the X-coordinate variation with jounce, calculated at the contact patch, as: </p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="text-align: left; text-indent: 23px; line-height: 1.28; margin: 0px 0px 11px 0px;"><img alt="drvsim_motioncueing_FormulaDeltaX" width="547" height="21" style="margin:0;width:547px;height:21px;border:none" src="drvsim_motioncueing_formuladeltax.png"/></p>
<p style="margin: 0px 0px 0px 23px;">Defining:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_06" width="562" height="54" style="margin:0;width:562px;height:54px;border:none" src="drvsim_aor_eq_06.png"/></p>
<p style="margin: 0px 0px 0px 23px;">&nbsp;</p>
<p style="margin: 0px 0px 0px 23px;">the pitch center location is estimated with:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_07" width="190" height="73" style="margin:0;width:190px;height:73px;border:none" src="drvsim_aor_eq_07.png"/><span class="f_ImageCaption"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  </span><span class="f_ImageCaption" style="font-size: 10pt; font-weight: normal;">Unit: </span><span class="f_ImageCaption" style="font-size: 10pt; font-style: italic; font-weight: normal;">[mm]</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;">&nbsp;</p>
<p style="margin: 0px 0px 0px 23px;">This formulation results in a generally good initial guess, and can be validated by running straight-line maneuvers in VI-CarRealTime.</p>
<p style="margin: 0px 0px 0px 23px;">Using the sensor point, available in the body subsystem of each car model, and placing it in the pitch center location found with the previous procedure, it is possible to check if and how much this point is moving while the vehicle changes its pitch angle displacement, aiming at virtually zero variations in X and Z directions.</p>
<p style="margin: 0px 0px 0px 23px;">To do that:</p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>place the sensor in the X and Z position found with the previous estimation</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>run a StraightBraking manouver with VI-CarRealTime</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>plot the results in VI-Animator, looking at the Sensor.Global_Z (m) values</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>If the Sensor.Global_Z increases with pitch, it means that the sensor is placed rearward respect to the real pitch center of the car; if the Sensor.Global_Z decreases with pitch, it means that the sensor is placed forward respect to the real pitch center of the car</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>Depending on the results, move the sensor in X direction in the VI-CarRealTime body subsystem and repeat the simulation</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 50px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span>iterate this process until you reach a good estimation of the pitch center: zero variation is never reached, since the pitch center position is moving during the braking phase, but a Sensor.Global_Z variation of maximum 8-10 mm is considered a good estimation.</p><p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">The pitch axis for the platform, to be inserted in VI-DriveSim interface, is finally computed with:</p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;"><img alt="drvsim_aor_eq_08" width="399" height="48" style="margin:0;width:399px;height:48px;border:none" src="drvsim_aor_eq_08.png"/> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Unit: <span style="font-style: italic;">[m]</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;"><span style="color: #000000;">&nbsp;</span></p>
<p style="margin: 0px 0px 0px 23px;">In this same block, the Tilt center of rotation can be set as well. This should be computed to tilt the driver around the head point w.r.t. the center of the platform top disk. It is typically set at the same X and Y coordinates as the hip point, with the Z coordinate increased by 0.7 ÷ 0.9 [m].</p>
<p class="p_Normal" style="margin: 0px 0px 0px 23px;">&nbsp;</p>

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